Cross Sections Perpendicular To The Y Axis

So pause this video and see if you can do that.

Cross sections perpendicular to the y axis. Find the volume of the solid whose base is the region inside the circle x 2 y 2 9 if cross sections taken perpendicular to the y axis are squares. If we take a slightly different view of the same three. Volumes with cross sections.

If the cross sections are perpendicular to the y axis then their areas will be functions of y denoted by a y in this case the volume v of the solid on a b is example 1. Volumes with cross sections. Similarly if the cross section is perpendicular to the y axis and its area is defined by the function a left y right then the volume of the solid from y c to y d is given by v int limits c d a left y right dy steps for finding the volume of a solid with a known cross section.

In this video we run through setting up an integral to give the volume of a solid whose cross sections perpendicular to the y axis are isosceles right triangles with a leg in the xy plane. Volume with cross sections perpendicular to y axis. For each y value the cross section of the solid taken perpendicular to the y axis is a rectangle whose base lies in r and whose height is y.

And in fact if you re not i encourage you to review that. Video transcript instructor you are likely already familiar with finding the area between curves.